Write a linear function

Learning Objectives Define and identify the slope and y-intercept of a linear function. Calculate the slope of a line given two points on the line. Write the equation of a linear function in slope-intercept form ($y = mx + b$) given its slope and y-intercept. Write the equation of a linear function in slope-intercept form given a point on the line and its slope. Write the equation of a linear function in slope-intercept form given two points on the line. Interpret the meaning of the slope and y-intercept in real-world contexts. Ever wonder how scientists predict the path of a hurricane 🌀 or how economists model stock market trends? Linear functions are often the first step! In this lesson, you'll learn how to 'write' or create the equation for a linear funct...

TermDefinitionExample Linear FunctionA function whose graph is a straight line. It describes a constant rate of change between two variables.The equation $y = 3x + 5$ represents a linear function. Slope ($m$)The measure of the steepness of a line; it represents the rate of change between the dependent and independent variables. It's often described as 'rise over run.'In $y = 2x + 1$, the slope is $2$, meaning for every 1 unit increase in $x$, $y$ increases by 2 units. Y-intercept ($b$)The point where the line crosses the y-axis. It represents the initial value or starting point when the independent variable ($x$) is zero.In $y = 2x + 1$, the y-intercept is $1$, so the line crosses the y-axis at the point $(0, 1)$. Slope-Intercept FormA common way to write linear equations,...

Slope Formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ Use this formula to calculate the slope ($m$) of a line when you are given two points $(x_1, y_1)$ and $(x_2, y_2)$ on the line. Slope-Intercept Form $y = mx + b$ This is the standard form for writing a linear function, where $m$ is the slope and $b$ is the y-intercept. Your goal is often to find $m$ and $b$ to write the equation in this form. Finding the Y-intercept ($b$) Substitute a known point $(x, y)$ and the calculated slope $m$ into the slope-intercept form $y = mx + b$, then solve the resulting equation for $b$. This method is used when the y-intercept is not directly given, but you have the slope and at least one point on the line.